\( 1 \leftarrow \begin{array}{l}\text { a. Rewnte the given equation } 5 x+7 y-35=0 \\ \text { slope-intercept form } \\ \text { b. Give the slope and } y \text {-intercept. } \\ \text { c Use the slope and } y \text {-intercept to graph the linear } \\ \text { function } \\ \text { a. The slope-intercept form of the equation is } \\ y=-\frac{5}{7} x+5 \\ \text { (Simplify your answer Use integers or fractions for any } \\ \text { numbers in the equation ) } \\ \text { b. The slope of the equation of the line is } \square \text { and } \\ \text { the } y \text {-intercept is } \square \\ \text { (Type integers or fractions ) }\end{array} \)

Let's solve the problem step by step. ### a. Rewrite the given equation in slope-intercept form The given equation is: \[ 5x + 7y - 35 = 0 \] To convert this to slope-intercept form \(y = mx + b\), we need to isolate \(y\). 1. Start by moving \(5x\) and \(-35\) to the other side: \[ 7y = -5x + 35 \] 2. Now, divide every term by \(7\) to solve for \(y\): \[ y = -\frac{5}{7}x + 5 \] So, the slope-intercept form of the equation is: \[ y = -\frac{5}{7}x + 5 \] ### b. Identify the slope and y-intercept From the slope-intercept form \(y = mx + b\): - The slope \(m\) is \(-\frac{5}{7}\). - The y-intercept \(b\) is \(5\). Thus, we have: - The slope of the equation of the line is \(-\frac{5}{7}\). - The y-intercept is \(5\). ### c. Use the slope and y-intercept to graph the linear function To graph the linear function: 1. **Plot the y-intercept**: Start at the point \((0, 5)\) on the y-axis. 2. **Use the slope**: The slope \(-\frac{5}{7}\) means that for every \(7\) units you move to the right (positive direction on the x-axis), you move \(5\) units down (negative direction on the y-axis). From the point \((0, 5)\): - Move \(7\) units to the right to \(x = 7\). - Move \(5\) units down to \(y = 0\). This gives you the point \((7, 0)\). 3. **Draw the line**: Connect the points \((0, 5)\) and \((7, 0)\) with a straight line, extending it in both directions. ### Summary of Answers - a. The slope-intercept form of the equation is \(y = -\frac{5}{7}x + 5\). - b. The slope of the equation of the line is \(-\frac{5}{7}\) and the y-intercept is \(5\).